Q9 of 32 Page 60

In figure 5.36 AB || CD, CD || EF and y : z = 3 : 7 then find the value of x.

Given:


AB || CD, CD || EF and y : z = 3 : 7


Theory:


⇒ If 2 lines are parallel then their corresponding angles are equal


⇒ If 2 lines are parallel then sum of their internal angles is 180°


If y : z = 3 : 7


Let ∠ y and ∠ z be 3a and 7a


As AB || EF


By alternate interior angles


∠ x = ∠ z


∠ x = 7a


As AB || CD


By interior angles


∠ x + ∠ y = 180°


7a + 3a = 180°


10a = 180°


⇒ a = = 18°


⇒ ∠ x = 7 × 18° = 126°


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